A-z-C-2-lt-z-lt-4-fine-log-A-where-log-is-complex-logaritmique-

Question Number 169918 by pticantor last updated on 12/May/22

A = {z \in C : 2 <∣ z ∣< 4}

f i n e l o g (A)

w h e r e l o g i s c o m p l e x l o g a r i t m i q u e

Answered by pticantor last updated on 12/May/22

b e s o i n d^{'} a i d e p l e a s e!!

Answered by Mathspace last updated on 12/May/22

w h a t m e a n l o g A \dots

Commented by pticantor last updated on 13/May/22

l o g A I s i m a g e o f A b y t h e {l o g a r i t h m i c}^{'} f o n c t i o n

a n d A i s t h e r i n g

o r

f : A \to C

z ↣ l o g (z)

f i n d l o g (A)

Answered by Mathspace last updated on 13/May/22

i f z = {r e}^{i θ} \Rightarrow∣ z ∣= r \Rightarrow 2 < r < 4

a n d l o g z = l o g r + i (θ + 2 k π) \Rightarrow

l o g A = {l o g r + i (θ + 2 k π) / k \in Z}

u n e d e t e r m i n a t i o n p r i n c i p a l e e s t

l o g r + i θ - π < θ < π

Commented by pticantor last updated on 13/May/22

j e c r o i s q u e v o u s a v e z j u s t e d o n n e r

l a d e f i n i t i o n d u l o g a r i t h m e c o m p l e x!

m a i s o n m e d e m a n d e l a n a t u r e d e l o g (A) e t l e

t r a c a g e d e l a c o u r b e